to see a world in a grain of sandwilliam blake, auguries of innocence

MARVEL

Human ages are named after materials: stone, bronze, iron, nuclear, silicon…

MATERIALS ARE KEY TO SOCIETAL WELL BEING

MARVEL

MATERIALS ARE KEY TO SOCIETAL WELL BEING

We need novel materials for:! Energy harvesting, conversion, storage, efficiency! Environmental protection and reparation! High-tech and high-value industries! Health care and biomedical engineering! Pharmaceuticals (crystallization, stability, polytypes)! Monitoring, provenance, and safety of foods ! Information and communication technologies! Fundamental science (graphene and 2D materials, topological

insulators, entangled spins for quantum computing, high-Tc)! Experimental science (detectors, sensors, magnets)

MARVEL

THE RISE OF MATERIALS SCIENCE

MARVEL

“The prize focuses on how to evaluate the variation in the energy of the realsystem in a accurate and efficient way […]. The Car–Parrinello approach isthe leading strategy along this line.”

“Simulations are so realistic that they predict the outcome of traditionalexperiments.”

From www.nobelprize.org/nobel_prizes/chemistry/laureates/2013/

THE RISE OF SIMULATION SCIENCE

MARVEL

MARVEL

Journal # cites Title Author(s)

1 PRB (1988) 39190 Development of the Colle-Salvetti Correlation-Energy … Lee, Yang, Parr

2 PRL (1996) 25452 Generalized Gradient Approximation Made Simple Perdew, Burke, Ernzerhof

3 PRA (1988) 22904 Density-Functional Exchange-Energy Approximation ... Becke

4 PR (1965) 20142 Self-Consistent Equations Including Exchange and Correlation … Kohn and Sham

5 PRB (1996) 13731 Efficient Iterative Schemes for Ab Initio Total-Energy … Kresse and Furthmuller

6 PRB (1976) 13160 Special Points for Brillouin-Zone Integrations Monkhorst and Pack

7 PRB (1992) 10876 Accurate and Simple Analytic Representation of the Electron … Perdew and Wang

8 PRB (1999) 10007 From Ultrasoft Pseudopotentials to the Projector Augmented … Kresse and Joubert

9 PRB (1990) 9840 Soft Self-Consistent Pseudopotentials in a Generalized … Vanderbilt

10 PR (1964) 9789 Inhomogeneous Electron Gas Hohenberg and Kohn

11 PRB (1981) 9787 Self-Interaction Correction to Density-Functional Approx. … Perdew and Zunger

12 PRB (1992) 9786 Atoms, Molecules, Solids, and Surfaces - Applications of the … Perdew, Chevary, …

13 PRB (1986) 9313 Density-Functional Approx. for the Correlation-Energy … Perdew

14 PR (1934) 9271 Note on an Approximation Treatment for Many-Electron Systems Moller and Plesset

15 PRB (1994) 9100 Projector Augmented-Wave Method Blochl

16 PRL (1980) 7751 Ground-State of the Electron-Gas by a Stochastic Method Ceperley and Alder

17 PRL (1987) 7663 Inhibited Spontaneous Emission in Solid-State Physics … Yablonovitch

18 PRL (1986) 7589 Atomic Force Microscope Binnig, Quate, Gerber

19 PRB (1991) 7425 Efficient Pseudopotentials for Plane-Wave Calculations Troullier and Martins

20 PRB (1993) 6925 Ab initio Molecular Dynamics for Liquid Metals Kresse and Hafner

21 PR (1961) 6467 Effects of Configuration Interaction on Intensities and Phase Shifts Fano

22 PR (1957) 6260 Theory of Superconductivity Bardeen, Cooper, Schrieffer

MOST CITED PAPERS IN APS (FROM 1893)

!"#$"#%&'()*+,

NATURE, October 2014

12 papers on DFTin the top-100 most cited papers in the

entire scientific literature, ever.

DFT reminder: First Hohenberg-Kohn theorem

The density as the basic variable: the external potential Vext determines uniquely the charge density, and the charge density determines

uniquely the external potential Vext.

1-to-1 mapping: Vext ⟺ "

The universal functional F[ρ]

The ground state density determines the potential of the Schrödinger equation, and thus the wavefunction.

The universal functional F is well defined:

Y+Y= -eeVTrF ˆˆ)]([ !r

Second Hohenberg-Kohn theorem

Ev[ρ(!r )] = F[ρ(!r )]+ vext (∫

!r )ρ(!r )d!r ≥ E0

The variational principle – we have a new Schrödinger’s-like equation, expressed in

terms of the charge density only

The Kohn-Sham mapping

F decomposed in non-interacting kinetic + Hartree + mistery

Fermi’s intuition: we construct Exc using the local density approximation (at every point we use the XC energy density of the non-interacting homogenous electron gas at that density)

MARVEL

MY BEST CALCULATION: 2 NOV 2010

http://quantum-espresso.org

MARVEL

A SMALL STEP FOR A CELLPHONE, A GIANT LEAP FOR COMPUTERKIND

!"#$%&'()(*"+(,-./

MARVEL

HIGH-THROUGHPUT SCREENING OF NOVEL MATERIALS

The number of inorganic materials known in full (i.e. with published structures) is ~200,000

Currently, basic properties can be calculated on the entire Piz Daint CSCS supercomputer (3th in the world) at the

tune of 1000 structures/minute.

MARVEL

GREAT ENTHUSIASM FOR MATERIALS DISCOVERY

MARVEL

MAJOR EFFORTS WORLDWIDE

2011 – US: the Materials Genome InitiativeMaterials Project (Berkeley), SUNCAT (Stanford), AFLOW (Duke), CHiMaD (NIST)

2014 – CH: 18 MCHF MARVEL (Computational Design and Discovery of Novel Materials)2015 – UK: 8.6 MGBP, Materials Computational Discovery Centre, U. Liverpool2015 – H2020: 14 M€, Centres of Excellence on materials’ simulations:

E-CAM – Simulation and Modelling; MaX – Materials Design at the Exascale;NoMaD – Novel Materials Discovery

2015 - US DOE: 60 M$, 5 Centers on Comp. Materials Science, 4 years renewable: U. Chicago, UC Berkeley, Rutgers, ORNL, USC

2016 – DK: 22 M$, Villum Centre for the Science of Sustainable Fuels and Chemicals (DTU Lyngby and Stanford)

2016 – US NSF: 35 M$, 2 Institutes on Scientific Software, 5 years: MolSSI (Stony Brook), Molecular Sciences Software Institute; SGCI (US San Diego) Science Gateways Community Institute

2017 - US Simons Foundation, 15 M$/year, Center on Computational Quantum Physics

2017 - US Toyota Research Institutes, 35 M$, Predictive Battery Performance

MARVEL

MARVEL MISSION STATEMENT

Accelerated design and discovery of novel materialsvia a materials’ informatics platform of

high-throughput simulations, powered by

1. advanced quantum simulations, for accuracy2. innovative sampling methods, to explore materials space3. materials informatics, to leverage data, machine learning

Materials for energy harvesting, storage, and conversion; ICT; high value/high tech, and organic crystals/pharma.

MARVEL

PHASE I 2014-18 (12 INST, 23 COMP, 3+15 EXP)

+ 15 experimental groups at PSI, EMPA, UNIGE, EPFL+ 15 experimental groups at PSI, EMPA, UNIGE, EPFLPSI, EMPA, UNIGE, EPFL

1) PREDICTIVE ACCURACY

2) REALISTIC COMPLEXITY

3) MATERIALS’ INFORMATICS

COMPUTATIONAL EXFOLIATION OFALL KNOWN INORGANIC MATERIALSCOMPUTATIONAL EXFOLIATION OF

ALL KNOWN INORGANIC MATERIALS

MARVEL

PHYSICS AND CHEMISTRY IN LOW DIMENSIONS

von Klitzing 1985

Laughlin, Störmer, Tsui 1989

Fert, Grünberg2007

Bednorz and Müller 1987 Geim and Novoselov2010

Ertl 2007

FertGrünberg2007

Binnig, Rohrer 1986

MARVEL

HIGH-THROUGHPUT COMPUTATIONAL EXFOLIATION

MARVEL

GEOMETRIC IDENTIFICATION OF LAYERED MATERIALS

Automation Data Environment Sharing

Automation Database Research environment SocialRemote management Provenance Scientific workflows SharingHigh-throughput Storage Data analytics Standards

http://www.aiida.netG. Pizzi et al., Comp. Mat. Sci. 111, 218 (2016)

MARVEL

!"#$%&%#'(#&)*#+&,-./0

MARVEL

!"#$%&'()%*#%+%,#"-&./%(*"0'*0"1

Primitive cell & structure sym. refinement

MARVEL

3D RELAXATION

Lowdimfinder on relaxed structure

Pw calculations

PwWorkflow

MARVEL

!"#$%&'()*(+%%$'$#),-)&.%)/0)!,$,1"2%+

ChronosWorkflow

MARVEL

!"#$%&'()#"*+,'&*,-)&'./,0&-&/&".

Stabilization procedureStabilization procedure

Γ-phonon calculation

Displace the atoms along the unstable eigenvectors

Final vc-relax

MARVEL

FINALLY…

MARVEL

!"##$%"&'(")&*+"'*(,$*%'($-"'.#*/.)0!

http://www.materialscloud.org

MARVEL

STABILITY ANALYSIS: MAGNETIC AND MECHANICAL

Band structures

Phonon dispersions

MARVEL

HOW MANY CANDIDATES? GEOMETRIC SCREENING

*At this level unicity is not tested

Unique to COD

Unique to ICSD

Common to both Total

Entries analyzed 307616 172370 479986*

CIF inputs 99212 87070 186282*

Unique 3D structures 60354 34548 13521 108423Layered 3D structures 1180 3257 1182 5619

MARVEL

Difference in interlayer distance when computed with/without vdW functionals (%)

! Eb < 30 meV/Å2 (DF2-C09) or Eb < 35 meV/Å2 (rVV10) ! 2D, easily exfoliable

! In-between! 2D, potentially exfoliable

! Eb > 130 meV/Å2 ! not 2D (discarded)

Easilyexfoliable

Potentiallyexfoliable

1036 monolayers

789 monolayers

Notexfoliable

HOW MANY CANDIDATES? GEOMETRIC SCREENING

https://www.materialscloud.org/discover/2dstructures

2D PROTOTYPES

MARVEL

JACUTINGAITE (Pt2HgSe3)

MARVEL

MONOLAYER JACUTINGAITE AS A KANE-MELE QSHI

A. Marrazzo et al., Phys. Rev. Lett. 120 117701 (2018)

� X �

�0.4

�0.2

0.0

0.2

0.4

Energy[eV]

0.5 eV band gap(G0W0+SOC)

1st NN not enough; 2nd NN interactions needed

2D children:

! High electron/hole mobility devices

! Topological insulators, quantum computing

! Ferromagnetic/spintronics in 2D

! Charge-density waves and superconductors

! Plasmonics, transparent conductors

3D layered parents:

! Solid-state ionic conductors

! Hydrogen or oxygen evolution catalysts

! Membranes for filtration/separation

! Piezo, ferro, and thermoelectrics

THERE IS PLENTY OF ROOM AT THE TOP

N. Mounet et al., Nature Nanotechnology 13, 246 (2018)

MARVEL

! From total energy to thermodynamics" temperature, pressure, chemical potentials and partial

pressures, electrochemical potential, pH

! Length, time, phase and composition sampling" linear scaling, multiscale," metadynamics, sketch-map" minima hopping, random-structure searches

! Complex properties" spectroscopies and microscopies: IR, Raman, XPS, XANES, NMR,

EPR, ARPES, STM, TEM…" composition-temperature phase diagrams" electronic and thermal transport: ballistic, Keldysh, Boltzmann" electron-hole interactions

COMPLEXITY

MARVEL

MULTISCALE TRANSPORT

! Nanoscale devices for !"#$%&'&#($%)"#*, +,-)(,!./&0"#&*

! Bulk or nanostructured (1&$!%&'&#($"#*(harvesting waste energy, cooling)

! Characterization via 2"$*(34$")#"4'&*.*4&#($%*#%4"&*

Source: Nature Materials

MARVEL

ELECTRICAL RESISTIVITY (TEMP, DOPING)

C.-H. Park et al., Nano Letters (2014)T. Y. Kim, C.-H. Park, and N. Marzari, Nano Letters (2016)

THEORY EXPTS (Kim 2010)

MARVEL

LINEARIZED BOLTZMANN EQUATION

Boltzmann transport equation

Phonon population at out-of-equilibrium conditions : equilibrium conditions :

Collision / scatteringoperator (linearised)

Diffusion / LiouvilleoperatorHeat flux:

Phonon population at equilibrium: index onall states

Collision / scatteringoperator (linearised)

Diffusion / Liouville

Hot Cold

MARVEL

Often, the Boltzmann equation is simplified with the single-mode relaxation time approximation (SMA), i.e. retaining the diagonal part of the scattering matrix:

!"#$#%&'&()")&*+#+,+-)'#.!"#/01#-%)#2&2*3$-4&"#"#5)6$,+#-&#)7*434894*'#:4-%#$#9)3$;$-4&"#-4')#$#%&'

RELAXATION-TIME APPROXIMATION

MARVEL

Often, the Boltzmann equation is simplified with the single-mode relaxation time approximation (SMA), i.e. retaining the diagonal part of the scattering matrix:

!"#$#%&'&()")&*+#+,+-)'#.!"#/01#-%)#2&2*3$-4&"#"#5)6$,+#-&#)7*434894*'#:4-%#$#9)3$;$-4&"#-4')#$#%&'

<-#+-)$5,#+-$-)

RELAXATION-TIME APPROXIMATION

() *#+# ,# -#%&'

=4")-46#-%)&9,>#)$6%#+6$--)94"(#3)$5+#-&#-%)9'$34+$-4&"

MARVEL

COMPOSITION DEPENDENCE IN Si1-xGex ALLOYS

!"#$%&'(#)"#*+,-,-(#*"#.+/-,012 %,3#)"#4%&/%&-(#5620"#789"#:8;;"#<=>??@

MARVEL

LAYERED MATERIALS

!"" #"" $""!""

!""

$""

# $%&'()*+

,-

!

."""

!"""

/"""

0"""

1""""

%&'()*&+,-,./

,0,123

234567879:;4<7323456:=7>?@*23456:=7

" #"" 4"" 5!"" 5$"" !"""6+1(+7*897+,.23

"

1.

1/

.":98':;'()*&+,-,./

,0,123

ABCC

$%&

0

!

!"" #"" $""!""

!""

$""

# $%&'()*+

,-

!

."""

!"""

/"""

0"""

1""""

%&'()*&+,-,./

,0,123

234567879:;4<7323456:=7>?@*23456:=7

" #"" 4"" 5!"" 5$"" !"""6+1(+7*897+,.23

"

1.

1/

.":98':;'()*&+,-,./

,0,123

ABCC

$%&

0

!

!"#$%&'(()*#+"#,-.-(()//0*#-/#'("#12'3)#4-//-56*#789:;

MARVEL

0 200 400 600 800Temperature (K)

10-9

10-8

10-7

10-6

10-5

10-4

Γ(cm-1)

Graphene

Linewidths for graphene, natural abundance, 100 μ

NORMAL PROCESSES DOMINATE

A. Cepellotti et al. (Nature Communications, 2015)

MARVEL

POISEUILLE AND ZIMAN HYDRODYNAMICS

0 200 400 600 800Temperature (K)

103

104

k(W

/mK)

Graphene

Poiseu

ille

Ziman

BallisticPoiseuilleZimanKinetic

Ballis

tic

Zim

an

Pois

euille

Kine

tic

0 200 400 600 800Temperature (K)

0

5000

10000

15000

20000

k(W

/mK)

Temperature (K)

k

Graphene

kL

kballisticL

k∞Representative

3D Solid

10 20 30

A. Cepellotti et al. (Nature Communications, 2015)

MARVEL 0 200 400 600 800

Temperature (K)103

104

k(W

/mK)

Graphene

Poiseu

ille

Ziman

BallisticPoiseuilleZimanKinetic

Ballis

tic

Zim

an

Pois

euille

Kine

tic

0 200 400 600 800Temperature (K)

0

5000

10000

15000

20000

k(W

/mK)

Temperature (K)

k

Graphene

kL

kballisticL

k∞Representative

3D Solid

10 20 30

POISEUILLE AND ZIMAN HYDRODYNAMICS

A. Cepellotti et al. (Nature Communications, 2015)

MARVEL

BREAKDOWN OF THE PHONON PICTURE

! the time scale of phonon scattering (i.e. the phonon lifetime) differs from that of heat flux dissipation;

! phonons are not the heat carriers;

! how can we define heat carriers and relaxation times?

To define heat carriers, !"#$%&'()&*%+"#,-"#+.&,,"/%)'#(0"/&,(/1

MARVEL

The rotated equation now is diagonal in the scattering part;we can extract time scales for heat flux dissipation!

FROM PHONONS TO RELAXONS

Express the Boltzmann equation in the new basis (!" is now thepopulation of relaxon α):

So, rather than phonons, we study the collision eigenvectors, that we will call !"#$%&'()

*)+,"-"##&../ $'0+1)+2$!3$!/4+567+89:;<=>+?/"@-&/'.+&'+

A..-(BCC-AD(/E()$-()&!FC$!./E#"(CGHC;;I

MARVEL

SUMMARY

MARVEL

100 101 102 103 104 105

Velocity (m/s)

10-6

10-5

10-4

10-3

10-2

10-1

100

101

Cont

ribut

ion

tok(

%)

relaxons

Graphene

phonons

spee

d of

sou

nd

VELOCITY SCALE

!"#$%&%''())* +,-#."#/+01+0*2#345#6789:;2#<"#=>+2#?"#@+,+A(0%2#!"#$%&%''())*2#."#/+01+0*2#+,-#!"#="#B%C+*'2#3.!D#6789:;

MARVEL

! Search for a wave solution for the phonon excitation numbers

! i.e. Laplace transform the LBTE

TRANSPORT WAVES IN THE LBTE

MARVEL

TRANSPORT WAVES IN THE LBTE

M K0

400

800

1200

1600

Freq

uenc

y (c

m-1

)

100 101 102 103 104 105

Decay time (ps)

A. Cepellotti and N. Marzari, PR Materials (2017)

MARVEL

TRANSPORT CONCLUSIONS

1. Thermal transport can be described accurately from first-principles

2. In layered or 2D materials the phonon picture breaks down, and hydrodynamicphenomena/collective excitations emerge

3. Relaxons as the individual carriers of heat4. Surface scattering as a friction effect5. Transport waves solutions for the LBTE –

generalization of second sound

MARVEL

2017 EPFL IBM PRIZE2018 APS METROPOLIS AWARD

THERMAL THANKS

Nicola Bonini (KCL), Cheol-Hwan Park (SNU), Giorgia Fugallo (Nantes),

Michele Lazzeri, Lorenzo Paulatto(Paris VI), Francesco Mauri (Roma)

Andrea Cepellotti(Berkeley)

MARVEL

Thanks for your attention

Nicolas Mounet Philippe Schwaller

Giovanni PizziAndrea CepellottiAndrius Merkys Ivano E. Castelli Nicola Marzari

Davide Campi Antimo Marrazzo Thibault Sohier

2D THANKS

MARVEL

ACKNOWLEDGMENTS

30+ in now in faculty positions and research labs worldwide:from Harvard to MIT, Imperial College, Seoul National...

MARVEL

Swiss National Centre for Computational Design and Discovery of Novel Materials

H2020 Centre of Excellence MaX: Materials Design at the Exascale

SNSFH2020 Nanoscience Foundries and Fine Analysis

H2020 European Materials Modelling CouncilH2020 Graphene Flagship

H2020 MarketplaceH2020 EPFL FellowsH2020 Marie Curie

Max-Planck-EPFL CentrePASC

PRACEConstelliumInnosuisse

SolvayVarinor

http://nccr-marvel.ch

http://max-centre.eu

ACKNOWLEDGMENTS

MARVEL

! It’s a very exciting and productive time for computational materials science

! Goals: Understand, predict, and design the properties and performance of novel or complex materials and devices

! Accuracy, complexity, and informatics

CONCLUSIONS

4 LAST WORDS OF ADVICE

1. Intelligence is over-rated –you need hard work, drive, vision, creativity

2. Life goes in a blink3. Your next few years are the

most critical4. You are getting one of the

best (academic) educations in the world